The necessity to process signals living in non-Euclidean domains, such as signals de- fined on the top of a graph, has led to the extension of signal processing techniques to the graph setting. Among different approaches, graph signal processing distinguishes it- self by providing a Fourier analysis of these signals. Analogously to the Fourier transform for time and image signals, the graph Fourier transform decomposes the graph signals in terms of the harmonics provided by the underlying topology. For instance, a graph signal characterized by a slow variation between adjacent nodes has a low frequency content. Along with the graph Fourier transform, graph filters are the key tool to alter the graph frequency content of a graph signal. This thesis focuses on graph filters that are performed distributively in the node domain–that is, each node needs to exchange in- formation ...

To the surprise of most of us, complexity in nature spawns from simplicity. No matter how simple a basic unit is, when many of them work together, the interactions among these units lead to complexity. This complexity is present in the spreading of diseases, where slightly different policies, or conditions,might lead to very different results; or in biological systems where the interactions between elements maintain the delicate balance that keep life running. Fortunately, despite their complexity, current advances in technology have allowed us to have more than just a sneak-peak at these systems. With new views on how to observe such systems and gather data, we aimto understand the complexity within. One of these new views comes from the field of graph signal processing which provides models and tools to understand and process data coming from such complex systems. With ...

The abundance of large and heterogeneous systems is rendering contemporary data more pervasive, intricate, and with a non-regular structure. With classical techniques facing troubles to deal with the irregular (non-Euclidean) domain where the signals are defined, a popular approach at the heart of graph signal processing (GSP) is to: (i) represent the underlying support via a graph and (ii) exploit the topology of this graph to process the signals at hand. In addition to the irregular structure of the signals, another critical limitation is that the observed data is prone to the presence of perturbations, which, in the context of GSP, may affect not only the observed signals but also the topology of the supporting graph. Ignoring the presence of perturbations, along with the couplings between the errors in the signal and the errors in their support, can drastically hinder ...

Acquisition is the first stage of a Global Navigation Satellite System (GNSS) receiver and has the goal to determine which signals are in view and provide rough estimates of the signal parameters. The main objective of the thesis was to provide a complete and cohesive analysis of the acquisition process clarifying different aspects often neglected in the literature. The thesis provides the statistical tools required for the characterization of the acquisition process. In particular, the signal presence is determined by searching several candidates for the signal code delay and Doppler frequency which define a cell of the acquisition search space. Thus, the acquisition process is characterized by the strategy adopted for searching for the signal parameters and the way a decision metric is compute for each cell of the search space. Given this observation, the thesis introduces the concepts of ...

Machine learning and deep learning techniques have emerged as powerful tools for addressing complex challenges across diverse domains. These methodologies are powerful because they extract patterns and insights from large and complex datasets, automate decision-making processes, and continuously improve over time. They enable us to observe and quantify patterns in data that a normal human would not be able to capture, leading to deeper insights and more accurate predictions. This dissertation presents two research papers that leverage these methodologies to tackle distinct yet interconnected problems in neuroimaging and computer vision for the quantification of human health. The first investigation, "Age prediction using resting-state functional MRI," addresses the challenge of understanding brain aging. By employing the Least Absolute Shrinkage and Selection Operator (LASSO) on resting-state functional MRI (rsfMRI) data, we identify the most predictive correlations related to brain age. Our study, ...

High dimensional time series data are observed in many complex systems. In networked data, some of the time series are influenced by other time series. Identifying these relations encoded in a graph structure or topology among the time series is of paramount interest in certain applications since the identifi ed structure can provide insights about the underlying system and can assist in inference tasks. In practice, the underlying topology is usually sparse, that is, not all the participating time series influence each other. The goal of this dissertation pertains to study the problem of sparse topology identi fication under various settings. Topology identi fication from time series is a challenging task. The first major challenge in topology identi fication is that the assumption of static topology does not hold always in practice since most of the practical systems are evolving ...

The cumulative impact of co-channel interferers, commonly referred to as aggregate network interference, is one of the main performance limiting factors in today’s mobile cellular networks. Thus, its careful statistical description is decisive for system analysis and design. A system model for interference analysis is required to capture essential network variation effects, such as base station deployment- and signal propagation characteristics. Furthermore it should be simple and tractable so as to enable first-order insights on design fundamentals and rapid exchange of new ideas. Interference modeling has posed a challenge ever since the establishment of traditional macro cellular deployments. The recent emergence of heterogeneous network topologies complicates matters by contesting many established aspects of time-honored approaches. This thesis presents user-centric system models that enable to investigate scenarios with an asymmetric interference impact. The first approach simplifies the interference analysis in a ...

Cellular Neural Networks are characterized by simplicity of operation. The network consists of a large number of nonlinear processing units; called cells; that are equally spread in the space. Each cell has a simple function (sequence of multiply-add followed by a single discrimination) that takes an element of a topographic map and then interacts with all cells within a specified sphere of interest through direct connections. Due to their intrinsic parallel computing power, CNNs have attracted the attention of a wide variety of scientists in, e.g., the fields of image and video processing, robotics and higher brain functions. Simplicity of operation together with the local connectivity gives CNNs first-hand advantages for tiled VLSI implementations with very high speed and complexity. The first VLSI implementation has been based on analogue technology but was small and suffered from parasitic capacitances and resistances ...

Video signals are sequences of natural images, where images are often modeled as piecewise-smooth signals. Hence, video can be seen as a 3D piecewise-smooth signal made of piecewise-smooth regions that move through time. Based on the piecewise-smooth model and on related theoretical work on rate-distortion performance of wavelet and oracle based coding schemes, one can better analyze the appropriate coding strategies that adaptive video codecs need to implement in order to be efficient. Efficient video representations for coding purposes require the use of adaptive signal decompositions able to capture appropriately the structure and redundancy appearing in video signals. Adaptivity needs to be such that it allows for proper modeling of signals in order to represent these with the lowest possible coding cost. Video is a very structured signal with high geometric content. This includes temporal geometry (normally represented by motion ...

In the world of Information and communications technology (ICT), strategies for innovation and development are increasingly focusing on applications that require spatial representation and real-time interaction with and within 3D-media environments. One of the major challenges that such applications have to address is user-centricity, reflecting e.g. on developing complexity-hiding services so that people can personalize their own delivery of services. In these terms, multimodal interfaces represent a key factor for enabling an inclusive use of new technologies by everyone. In order to achieve this, multimodal realistic models that describe our environment are needed, and in particular models that accurately describe the acoustics of the environment and communication through the auditory modality are required. Examples of currently active research directions and application areas include 3DTV and future internet, 3D visual-sound scene coding, transmission and reconstruction and teleconferencing systems, to name but ...

Automatic face recognition has attracted a lot of attention not only because of the large number of practical applications where human identification is needed but also due to the technical challenges involved in this problem: large variability in facial appearance, non-linearity of face manifolds and high dimensionality are some the most critical handicaps. In order to deal with the above mentioned challenges, there are two possible strategies: the first is to construct a “good” feature space in which the manifolds become simpler (more linear and more convex). This scheme usually comprises two levels of processing: (1) normalize images geometrically and photometrically and (2) extract features that are stable with respect to these variations (such as those based on Gabor filters). The second strategy is to use classification structures that are able to deal with non-linearities and to generalize properly. To ...

In Wireless Sensor Networks (WSN), the ability of sensor nodes to know its position is an enabler for a wide variety of applications for monitoring, control, and automation. Often, sensor data is meaningful only if its position can be determined. Many WSN are deployed indoors or in areas where Global Navigation Satellite System (GNSS) signal coverage is not available, and thus GNSS positioning cannot be guaranteed. In these scenarios, WSN may be relied upon to achieve a satisfactory degree of positioning accuracy. Typically, batteries power sensor nodes in WSN. These batteries are costly to replace. Therefore, power consumption is an important aspect, being performance and lifetime ofWSN strongly relying on the ability to reduce it. It is crucial to design effective strategies to maximize battery lifetime. Optimization of power consumption can be made at different layers. For example, at the ...

Hyperspectral (HS) imaging, which consists of acquiring a same scene in several hundreds of contiguous spectral bands (a three dimensional data cube), has opened a new range of relevant applications, such as target detection [MS02], classification [C.-03] and spectral unmixing [BDPD+12]. However, while HS sensors provide abundant spectral information, their spatial resolution is generally more limited. Thus, fusing the HS image with other highly resolved images of the same scene, such as multispectral (MS) or panchromatic (PAN) images is an interesting problem. The problem of fusing a high spectral and low spatial resolution image with an auxiliary image of higher spatial but lower spectral resolution, also known as multi-resolution image fusion, has been explored for many years [AMV+11]. From an application point of view, this problem is also important as motivated by recent national programs, e.g., the Japanese next-generation space-borne ...

The first part of this dissertation considers distributed learning problems over networked agents. The general objective of distributed adaptation and learning is the solution of global, stochastic optimization problems through localized interactions and without information about the statistical properties of the data. Regularization is a useful technique to encourage or enforce structural properties on the resulting solution, such as sparsity or constraints. A substantial number of regularizers are inherently non-smooth, while many cost functions are differentiable. We propose distributed and adaptive strategies that are able to minimize aggregate sums of objectives. In doing so, we exploit the structure of the individual objectives as sums of differentiable costs and non-differentiable regularizers. The resulting algorithms are adaptive in nature and able to continuously track drifts in the problem; their recursions, however, are subject to persistent perturbations arising from the stochastic nature of ...

The localization and tracking of sound sources using microphone arrays is a problem that, even if it has attracted attention from the signal processing research community for decades, remains open. In recent years, deep learning models have surpassed the state-of-the-art that had been established by classic signal processing techniques, but these models still struggle with handling rooms with strong reverberations or tracking multiple sources that dynamically appear and disappear, especially when we cannot apply any criteria to classify or order them. In this thesis, we follow the ideas of the Geometric Deep Learning framework to propose new models and techniques that mean an advance of the state-of-the-art in the aforementioned scenarios. As the input of our models, we use acoustic power maps computed using the SRP-PHAT algorithm, a classic signal processing technique that allows us to estimate the acoustic energy ...